TITLE:
Applications of Homomorphism on the Structure of Semigroups
AUTHORS:
Huishu Yuan, Xiangzhi Kong
KEYWORDS:
Homomorphism; Natural Partial Order; Green’s (*, ~) -Relation; Semilattice Decomposition
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.2,
February
28,
2014
ABSTRACT:
By utilizing homomorphisms and -strong semilattice of semigroups, we show that the
Green (*,~)-relation H*,~ is a regular
band congruence on a r-ample semigroup if and only if it is a G-strong semilattice of completely J*,~-simple semigroups. The result generalizes Petrich’s result
on completely regular semigroups with Green’s relation H a normal band
congruence or a regular band congruence from the round of regular semigroups to
the round of r-ample semigroups.